Q.16. Define interquartile range.
Ans. Interquartile range is the difference between the third (Q_{3}) and first (Q_{1}) quartile of a series.
Q.17. How does the calculation of range differ for a discrete series and a continuous series?
Ans. In a discrete series, range is the difference between the highest value and the lowest value in a series. For a continuous series, on the other hand, range is calculated as the difference between the upper limit of the highest class and the lower limit of the lowest class.
Q.18. What are the advantages of quartile deviation as a measure of dispersion?
Ans. Following are the merits of quartile deviation: (i) It is very simple to calculate and understand. (ii) Quartile deviation is not affected by extreme values of the series. (iii) It can be calculated for openended frequency distribution.
Q.19. State the demerits of quartile deviation.
Ans. Following are the demerits of quartile deviation:
(i) It is not based on all the values of the series.
(ii) It is not suitable for further algebraic testing.
(iii) It is affected by fluctuations in sample.
Q.20. Define mean deviation.
Ans. Mean deviation is the arithmetic average of the deviations of all the values taken from average value (mean or median) of the series.
Q.21. Why is mode not used to calculate mean deviation?
Ans. Mode is not used to calculate mean deviation because it is not a stable average.
Q.22. What are the merits and demerits of mean deviation?
Ans. Merits of Mean Deviation
(i) It is simple to calculate and easy to understand.
(ii) Mean deviation is not affected by extreme values.
(iii) It is based on all the items of the series and hence, is more representative than range or quartile deviation.
Demerits of Mean Deviation
(i) Mean deviation is not capable of any further mathematical treatment.
(ii) Mean deviation suffers from inaccurate results as it ignores algebraic sign in calculation.
Q.23. Write the merits and demerits of standard deviation.
Ans. Merits of Standard Deviation:
(i) It is based on all the values of series.
(ii) It is least affected by the changes in the sample.
(iii) It is a clear and definite measure of dispersion.
(iv) It is capable of further mathematical treatment.
Demerits of Standard Deviation:
(i) It is a very lengthy and difficult process.
(ii) Since it is calculated with the help of mean, it is affected by extreme values.
Q.24. State the important properties of standard deviation.
Ans. Following are the important properties of standard deviation:
(i) Standard deviation is independent of origin, that is, it is not affected by the constant from which deviations are taken.
(ii) Standard deviation is not independent of scale, that is, if the deviations are divided by a common factor, its value is used in the formula to get the obtain standard deviation.
Q.25. What is Lorenz curve?
Ans. Lorenz curve is the graphical representation of dispersion. It compares the variability of two or more distributions.
Q.26. What does Lorenz curve indicate?
Ans. Lorenz curve indicates the degree of variability through the information expressed in a cumulative form.
Q.27. How does Lorenz curve analyse dispersion?
Ans. When there are two or more curves, the one which is the farthest from line of equal distribution has the highest dispersion.
Q.28. Discuss the application of Lorenz curve.
Ans. Lorenz curve is a graphical method of studying dispersion. The main aim of constructing a Lorenz curve is to study the degree of inequality in two or more distributions. It was mainly introduced to study the distribution of wealth and income. However, it became popular to study the variability in the distribution of profits, wages, revenue, population, etc.
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